Linear algebra (Fall 2010)

Time: M,W,F 10:00-11:00

Room: Creative Building 412

Exams:

Lecture assistant: 임상섭 ekdn123 at kaist  ac kr  오정석 ojs0603 at kaist ac kr

(There will be exercise sessions organized by the TA.)

Important notice: Those people who do not take the midterm or final exam will be given F.
Those students who do not take more than 30% of the quizzes will be given F. 

Grade distributions: A:30%, B:40%, C or below 30%. (I will include the people who drop the course.)

Lecturer: Suhyoung Choi at Room E6-4403

schoi at math dot kaist dot ac dot kr

This course begins abstract mathematics and is a good introduction to all the methods of
modern abstract mathematics. This course is your finest initiation into abstract thinking which you won’t find
in any other course in the universities today. So take this opportunity to develop this mode of
thinking. Having taken a previous course on logic and the set theory would be very helpful for you.
I wrote and linked some help at  http://math.kaist.ac.kr/~schoi/teaching.html
(My advice is that college does last only four years and after that you can probably choose to
work in areas that do not require abstract thinking if you don’t like it. )
(Of course, one should not think that pure mathematics helps you at all in making money.)

This course concentrates on justifying the linear algebra theorems and procedures with
proofs, definitions and so on. You will learn to prove some theorems here.
(A part of the purpose of this course is to introduce you to proving theorems, lemmas,
and corollaries.)

You are expected to have prepared for the lecture by reading ahead and solving
some of the problems. Reading books is very important for you.


Course Book:  Linear algebra 2nd Edition by Hoffman and Kunz Prentice Hall (Despite the fact that
this book is kind of hard to read for you but it is the only book left on earth with the content we need in this department.)

Helpful references:

Paul R. Halmos, Finite dimensional vector spaces, UTM, Springer (mostly theoretical)
B. Hartley, Rings, Modules, and Linear Algebra, Chapman and Hall
Larry Smith, Linear Algebra, 2nd Edition, Springer (Similar to our book, But fields are either the real field or
the complex field.)
Seldon, Axler, Linear algebra done right, Springer (Similar, Same field restriction as above)
S. Friedberg et al., Linear algebra 4th Edition, Prentice Hall (Most similar to our book. More
concrete. weak in theoretical side.)
Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, MA, USA
Two Korean books of almost the same content as Hoffman-Kunz:
선형대수학, 김응태, 박승안 공저, 청문7.4, 7.1rtment.)ad for you but it is the only book with the content we need in this department.)   7.4, 7.1rtment.)ad for you but it is the only book with the content we need in this department.)
선형대수학. 임긍빈, 임동만, 형실출판사  

Grades: Midterm(150pts) Final(150pts) Quiz (100pts) Class participation (50pts)
Total 450pts

Exams will be given according to the KAIST schedule. There are old exams at math.kaist.ac.kr/~schoi/teaching.html.

Quizzes: There will be a quiz almost every week. There will be one or two problems to solve
given 20 minutes. The quiz problems are very similar or identical with the homework problems.
One should prepare for them by groups of students working on homework problems together.
The homework problems are not to be turned in.

Introduction to formal mathematical proofs

Chapter 1: Linear equations

Chapter 2: Vector spaces

Chapter 3: Linear transformations

Chapter 4: Polynomials

Midterm

Chapter 5: Determinants

Chapter 6: Elementary canonical forms

Chapter 7: The rational and Jordan forms

Final

 

The teaching homepage:

http://math.kaist.ac.kr/~schoi/teaching.html

Course homepage: mathsci.kaist.ac.kr, math.kaist.ac.kr/~schoi/linearalg2008I.htm

 

Monday

 

Wednesday

 

Friday

 


 

9/1

Introduction to linear algebra

9/3

1.1,1.2.1.3,1.4.

9/6

1.5,1.6.

9/8

2.1

9/10

2.2

9/13

2.3

9/15

2.3.

9/17

2.4

9/20

2.5.

9/22

Holiday

9/24

2.6.

9/27

3.1.

9/30

3.2.

10/1

3.3.

10/4

3.4.,3.5

10/6

3.6.

10/8

4.1,4.2.

10/11

4.3.

10/13

4.4.

10/15

4.4.

10/18

4.5

10/20

midterm

10/22

midterm

10/25

midterm

10/27

5.1, 5.2

10/29

5.3

11/1

5.4.

11/3

6.1,6.2.

11/5

6.2

11/8

6.3.

11/10

6.3

11/12

6.4.

11/15

6.4

11/17

6.6.

11/19

6.7.

11/22

6.8.

11/24

6.8

11/26

7.1

11/29

7.2.

12/1

7.2.

12/3

7.3

12/6

7.3

12/8

7.4.

12/10

7.4

12/13

Q&A session

12/15

final

12/17

final

 

 

 

 

 

 

 

 

 

 

 

 

 

MIT Linear algebra class (This correspond to our course exactly.)

Harvard Linear algebra class (correspond to our course)

Homework sets: Do not turn in your works but you should know how to solve these problems.
For quizzes, the teaching assistants will make problems similar to these. The best way is
to study the problems that were taught on that day.

S.1.2:p.5:1,4,5, S.1.3:p.10:2,p.11:4,8, S.1.4: p.16:4,6,

S.1.5: p.21:1,6, S.1.6: p.26:3,6,7, S.2.1:p.33:1, p.34:4,6, S.2.2: p.39:1,2, p.40:6,8,

S.2.3:p.48:2,3,6, p.49:11, S.2.4:p.55:3,4,6.

S.2.6:p.66:1,3,5, S. 3.1:p.73:1,3,7,9, S.3.2:p.83:1,3,5, p.84:7.

S.3.3:p.86:2,3,S.3.4:p.95:2,5,7, S.3.5:p.105:1,2,4,7, p.106:9,11,12.

S.3.6: p.111: 1,2, S.4.2: p.123:2,4,7,9, S.4.3:p.126:1,2,3.

S.4.4:p.134:1,2,4, S.4.5:p.139:2,3

S.5.2:p.148:1, p.149:8,9,10, S.5.3:p.155:2,4,7, p.156:11.

S.5.4:p.162:1,3, p.163:7,9,12, S.6.2:p.189:1,3,5, p.190:6,10,11, S.6.3:p.198:3,4,6,8.

S.6.4:p.205:1,3,4,5,9, p.206:11,12, S.6.6:p.213: 1,2,3,8.

S.6.7:p.218:1,2, p.219: 4,5,9, S.6.8:p.225:1,2, p.226:5,9

S.7.1:p.230:1,2,3, p.231:6,7, S.7.2:p.241:1,2,3, p.242: 4,8,9,p.243:11,12. (13th and 14th week together)

S.7.3:p.250:3,6,7,8, S.7.4:p.261:4.